ObjectANCFThinPlate

OBJECT UNDER CONSTRUCTION: A 3D thin Kirchhoff plate finite element based on the absolute nodal coordinate formulation, using 4 nodes of type NodePointSlope12. The geometry as well as (deformed and distorted) reference configuration is given by the nodes. The localPosition follows unit-coordinates in the range [-1,1] for X, Y and Z coordinates; the thickness of the plate is h; This element is under construction.

Additional information for ObjectANCFThinPlate:

  • This Object has/provides the following types = Body, MultiNoded
  • Requested Node type = Position

The item ObjectANCFThinPlate with type = ‘ANCFThinPlate’ has the following parameters:

  • name [type = String, default = ‘’]:
    objects’s unique name
  • physicsThickness [\(h\), type = NumpyVector, default = []]:
    [SI:m] thickness of plate either provided as scalar or as vector (4 values, same order as local element node numbers) values that are linearly interpolated from nodal values; dimensionality must agree between thickness, strainCoefficients and curvatureCoefficients
  • physicsDensity [\(\rho\), type = UReal, default = 0.]:
    [SI:kg/m\(^3\)] density of the plate, possibly averaged over thickness
  • physicsMassProportionalDamping [type = Real, default = 0.]:
    mass-proportional damping coefficient \(\alpha\) [SI:1/s]; adds massmatrix proportional damping forces \({\mathbf{f}}_d = \alpha {\mathbf{M}} \dot{{\mathbf{q}}}\)
  • physicsStrainCoefficients [\({\mathbf{D}}_\varepsilon\), type = Matrix3DList, default = []]:
    [SI:N/m] stiffness coefficients related to inplane normal and shear strains, integrated over height of the plate; either given as 3D Matrix (numpy array), or a list of 3D matrices at each nodal point, see thickness; dimensionality must agree between thickness, strainCoefficients and curvatureCoefficients
  • physicsCurvatureCoefficients [\({\mathbf{D}}_\kappa\), type = Matrix3DList, default = []]:
    [SI:Nm] stiffness coefficients related to curvatures, integrated over height of the plate; either given as 3D Matrix (numpy array), or a list of 3D matrices at each nodal point, see thickness; dimensionality must agree between thickness, strainCoefficients and curvatureCoefficients
  • strainIsRelativeToReference [\(f\cRef\), type = Real, default = 1.]:
    if set to 1., a pre-deformed reference configuration is considered as the stressless state; if set to 0., the straight configuration serves as a reference geometry; allows also values between 0. and 1. to perform a transition during static computation
  • slopesScalingX [type = Vector4D, size = 4, default = [-1.,-1.,-1.,-1.]]:
    scaling of x-slopes at each element node; flat elements: half of the side length of the element; curved: optimal values such that curved geometry is best approximated; if negative (default) values are used, length is computed from node distances.
  • slopesScalingY [type = Vector4D, size = 4, default = [-1.,-1.,-1.,-1.]]:
    scaling of y-slopes at each element node; flat elements: half of the side length of the element; curved: optimal values such that curved geometry is best approximated; if negative (default) values are used, length is computed from node distances.
  • nodeNumbers [type = NodeIndex4, default = [invalid [-1], invalid [-1], invalid [-1], invalid [-1]]]:
    4 NodePointSlope12 node numbers, with local (xi,eta) coordinates as [(-1,-1),(1,-1),(1,1),(-1,1)]
  • useReducedOrderIntegration [type = Index, default = 0]:
    0/false: use highest Gauss integration for virtual work of strains
  • visualization [type = VObjectANCFThinPlate]:
    parameters for visualization of item

The item VObjectANCFThinPlate has the following parameters:

  • show [type = Bool, default = True]:
    set true, if item is shown in visualization and false if it is not shown; note that all quantities are computed at the beam centerline, even if drawn on surface of cylinder of beam; this effects, e.g., Displacement or Velocity, which is drawn constant over cross section
  • color [type = Float4, default = [-1.,-1.,-1.,-1.]]:
    RGBA color of the object; if R==-1, use default color

DESCRIPTION of ObjectANCFThinPlate

The following output variables are available as OutputVariableType in sensors, Get…Output() and other functions:

  • Position: \(\LU{0}{{\mathbf{p}}\cConfig(x,y,z)}\)
    global position vector of local position \([x,y,z]\)
  • Displacement: \(\LU{0}{{\mathbf{u}}\cConfig(x,y,z)} = \LU{0}{{\mathbf{p}}\cConfig(x,y,z)} - \LU{0}{{\mathbf{p}}\cRef(x,y,z)}\)
    global displacement vector of local position
  • Velocity: \(\LU{0}{{\mathbf{v}}(x,y,z)} = \LU{0}{\dot {\mathbf{r}}(x,y,z)}\)
    global velocity vector of local position
  • Director1: \({\mathbf{r}}_x(x,y,z)\)
    (axial) slope vector of local position (at \(z\)=0)
  • Director2: \({\mathbf{r}}_y(x,y,z)\)
    (axial) slope vector of local position (at \(z\)=0)
  • StrainLocal: \(\varepsilon\)
    axial strain (scalar) of local axis position (at Z=0)
  • CurvatureLocal: \([K_x, K_y, K_z]\tp\)
    local curvature vector
  • ForceLocal: \(N\)
    (local) section normal force per length (scalar, including reference strains) (at \(z\)=0)
  • TorqueLocal: \(M\)
    (local) bending moment per length (scalar) (at \(z\)=0), which are bending moments as there is no torque
  • StressLocal:
    local inplane stress components
  • Acceleration: \(\LU{0}{{\mathbf{a}}(x,y,z)} = \LU{0}{\ddot {\mathbf{r}}(x,y,z)}\)
    global acceleration vector of local position

Note: For output variables, the localPosition is defined in \([-1,-1,-1] ... [1,1,1]\), where \([-1,-1,0]\) is the position of node 0.

MINI EXAMPLE for ObjectANCFThinPlate

#to be done

#check result
exudynTestGlobals.testResult = 0

The web version may not be complete. For details, consider also the Exudyn PDF documentation : theDoc.pdf